Template for Project 1 Data Analysis Report (replace it with your own title)
Zeng Fung Liew (913802324),
February 2, 2021
1 Introduction
2 Background
3 Descriptive analysis
3.1 Overview
3.2 Exploratory Analysis
3.2.1 Univariate Analysis
3.2.1.1 Predictor Variables
3.2.1.2 Response Variables
3.2.2 Multivariate Analysis
4 Inferential analysis
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## unemp -0.0567273 0.0071020 -7.9875 3.715e-14 ***
## jailyes -0.0075778 0.1245342 -0.0608 0.9515232
## drinkage19 -0.0421462 0.0662733 -0.6359 0.5253372
## drinkage20 -0.0223700 0.0726344 -0.3080 0.7583287
## drinkage21 0.0520453 0.0696946 0.7468 0.4558406
## beertax -0.5877703 0.1716524 -3.4242 0.0007099 ***
## spirits 0.6944051 0.0802470 8.6533 4.154e-16 ***
## dry 0.0279848 0.0134966 2.0735 0.0390522 *
## serviceyes 0.0361896 0.1439526 0.2514 0.8016915
## breathyes 0.0206776 0.0506726 0.4081 0.6835426
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = fatal_r ~ unemp + jail + drinkage + beertax + spirits +
## dry + service + breath, data = data, model = "within", index = c("state",
## "year"))
##
## Unbalanced Panel: n = 48, T = 6-7, N = 335
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.4718637 -0.0788562 0.0018826 0.0794093 0.6230710
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## unemp -0.0567273 0.0071020 -7.9875 3.715e-14 ***
## jailyes -0.0075778 0.1245342 -0.0608 0.9515232
## drinkage19 -0.0421462 0.0662733 -0.6359 0.5253372
## drinkage20 -0.0223700 0.0726344 -0.3080 0.7583287
## drinkage21 0.0520453 0.0696946 0.7468 0.4558406
## beertax -0.5877703 0.1716524 -3.4242 0.0007099 ***
## spirits 0.6944051 0.0802470 8.6533 4.154e-16 ***
## dry 0.0279848 0.0134966 2.0735 0.0390522 *
## serviceyes 0.0361896 0.1439526 0.2514 0.8016915
## breathyes 0.0206776 0.0506726 0.4081 0.6835426
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 10.785
## Residual Sum of Squares: 7.3356
## R-Squared: 0.31982
## Adj. R-Squared: 0.17986
## F-statistic: 13.0247 on 10 and 277 DF, p-value: < 2.22e-16##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## unemp -0.0133817 0.0055587 -2.4073 0.01672 *
## jailyes 0.2039941 0.0974724 2.0928 0.03727 *
## drinkage19 0.0370111 0.0518718 0.7135 0.47613
## drinkage20 0.0122483 0.0568506 0.2154 0.82958
## drinkage21 0.0302554 0.0545496 0.5546 0.57959
## beertax -0.2039728 0.1343515 -1.5182 0.13010
## spirits 0.3989548 0.0628089 6.3519 8.692e-10 ***
## dry 0.0048993 0.0105637 0.4638 0.64316
## serviceyes -0.1983558 0.1126710 -1.7605 0.07943 .
## breathyes -0.0152399 0.0396612 -0.3843 0.70109
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = afatal_r ~ unemp + jail + drinkage + beertax +
## spirits + dry + service + breath, data = data, model = "within",
## index = c("state", "year"))
##
## Unbalanced Panel: n = 48, T = 6-7, N = 335
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.9489734 -0.0571550 -0.0073183 0.0504910 0.4753808
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## unemp -0.0133817 0.0055587 -2.4073 0.01672 *
## jailyes 0.2039941 0.0974724 2.0928 0.03727 *
## drinkage19 0.0370111 0.0518718 0.7135 0.47613
## drinkage20 0.0122483 0.0568506 0.2154 0.82958
## drinkage21 0.0302554 0.0545496 0.5546 0.57959
## beertax -0.2039728 0.1343515 -1.5182 0.13010
## spirits 0.3989548 0.0628089 6.3519 8.692e-10 ***
## dry 0.0048993 0.0105637 0.4638 0.64316
## serviceyes -0.1983558 0.1126710 -1.7605 0.07943 .
## breathyes -0.0152399 0.0396612 -0.3843 0.70109
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 5.3854
## Residual Sum of Squares: 4.4939
## R-Squared: 0.16555
## Adj. R-Squared: -0.0061595
## F-statistic: 5.49553 on 10 and 277 DF, p-value: 1.8671e-075 Sensitivity analysis
6 Causal interpretation
In panel data, measures were conducted on the same entity (state) repeatedly at different time points (years). Also, the fixedd effect model adopted in the current project accounted for unobserved, entity-specific, time-invariant confounders. Given these features, it might seem reasonble to make causal inference for significant predictors on the response variable. However, a fixed effect model requires strong exogeneity assumptions in order to make causal inference, including: (a) no unobserved time-varying confounders; (b) past outcomes do not directly affect current outcome; (c) past treatments do not directly affet current outcome; (d) past outcome do not directly affect current treatment (reverse causation).
Assumption (a) is hard to verify and also difficult to relax under the fixed effect model. Thus we assumed no time-varying covariates were omitted from the current model and see whether the other assumptions were violated in the current model and how they can be relaxed. Assumption (b) can be relaxed without interfering with the causal inference between current treatment and current outcome so long as we condition on past treatment, and assuming past outcome does no directly affect current treatment. To relax assumption (c), we could add a small number of lagged treatment effect into the model (e.g. treatment from the year before). Last, for assumption (d): no reverse causation, a popular approach to relax it is to include instrumental variables for endogenous predictors. Endogenous predictors are those included in the model but are correlated with the error term. This could happen when the response variable can reversely cause the predictor, or some omitted confounders can affect both dependent and independent variables. Instrumental variables were those not included in the model, associated with the endogenous predictor, but not associated with the unobserved confounders.
Some previous studies on the traffic policy environment and fatality rate suggested using alcohol regulations as instrumental variables for alcohol consumption when investigating the effect of alcohol consumption on traffic accidents fatality. Such alcohol regulations can only affect traffic accident fatality through alcohol consumption, and there were previous studies showing significant effect of such regulations on alcohol consumption. In the current dataset, the covariate related to alcohol consumption is "spirits", and alcohol regulations include "drinkage" (minimum drinking age), and "beertax". To verify the approporiateness of drinkage and beertax as instrumental variables for spirits consumption, under-identification, weak instrument, and over-identification need to be tested. To test for under-identification is to test the null hypothesis that spirits and beertax or drink age are irrelevant. This could be done through simple t-test and likelihood ratio test. The result showed that beertax was not associated with spirits consumption (Pr(>F) = 0.1012), but drinkage had significant effect (Pr(>F) <0.0001). Thus, beertax failed the under-idetification test. Weak instrument was tested by calculating Cragg-Donald F statistic and comparing it against Stock and Yogo critical values. The null hypothesis (the instrumental variables are weak) can be rejected if the Crgg-Donald F statistic is greater than the criticla value. The Cragg-Donald F statistic calculated for drinkage was 10.59, and the critical value was 22.3, thus we failed to reject the null at significance level 0.05. As a result, we could not find appropriate instrumental variables for spirits in the current dataset. If more measures are availble, such as other alcohol regulations and other alcohol consumption information, we might be able to find more suitable instrument variables.
7 Discussion
Acknowledgement
Reference
Session info
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.4
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] grid stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] plm_2.4-0 gplots_3.1.1 panelr_0.7.5 lme4_1.1-26
## [5] Matrix_1.2-18 GGally_2.1.0 forcats_0.5.0 stringr_1.4.0
## [9] dplyr_1.0.2 purrr_0.3.4 readr_1.4.0 tidyr_1.1.2
## [13] tibble_3.0.4 tidyverse_1.3.0 plotly_4.9.3 ggplot2_3.3.3
## [17] AER_1.2-9 survival_3.2-7 sandwich_3.0-0 lmtest_0.9-38
## [21] zoo_1.8-8 car_3.0-10 carData_3.0-4
##
## loaded via a namespace (and not attached):
## [1] nlme_3.1-149 bitops_1.0-6 fs_1.5.0 lubridate_1.7.9.2
## [5] RColorBrewer_1.1-2 httr_1.4.2 tools_4.0.3 backports_1.2.1
## [9] R6_2.5.0 KernSmooth_2.23-17 DBI_1.1.0 lazyeval_0.2.2
## [13] colorspace_2.0-0 withr_2.3.0 tidyselect_1.1.0 gridExtra_2.3
## [17] curl_4.3 compiler_4.0.3 cli_2.2.0 rvest_0.3.6
## [21] xml2_1.3.2 labeling_0.4.2 caTools_1.18.1 scales_1.1.1
## [25] digest_0.6.27 minqa_1.2.4 foreign_0.8-80 rmarkdown_2.6
## [29] rio_0.5.16 pkgconfig_2.0.3 htmltools_0.5.0 dbplyr_2.0.0
## [33] htmlwidgets_1.5.3 rlang_0.4.10 readxl_1.3.1 rstudioapi_0.13
## [37] generics_0.1.0 farver_2.0.3 jsonlite_1.7.2 gtools_3.8.2
## [41] crosstalk_1.1.1 zip_2.1.1 magrittr_2.0.1 Formula_1.2-4
## [45] Rcpp_1.0.5 munsell_0.5.0 fansi_0.4.1 abind_1.4-5
## [49] lifecycle_0.2.0 stringi_1.5.3 yaml_2.2.1 gbRd_0.4-11
## [53] MASS_7.3-53 plyr_1.8.6 bdsmatrix_1.3-4 crayon_1.3.4
## [57] lattice_0.20-41 haven_2.3.1 splines_4.0.3 pander_0.6.3
## [61] jtools_2.1.2 hms_0.5.3 knitr_1.30 pillar_1.4.7
## [65] boot_1.3-25 reprex_0.3.0 glue_1.4.2 evaluate_0.14
## [69] data.table_1.13.6 modelr_0.1.8 Rdpack_2.1 nloptr_1.2.2.2
## [73] vctrs_0.3.6 miscTools_0.6-26 cellranger_1.1.0 gtable_0.3.0
## [77] reshape_0.8.8 assertthat_0.2.1 xfun_0.19 openxlsx_4.2.3
## [81] rbibutils_2.0 broom_0.7.3 viridisLite_0.3.0 maxLik_1.4-6
## [85] statmod_1.4.35 ellipsis_0.3.1